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Evaluating Flexible Pavement Rut Damage
Caused by Multiple Axle and TruckConfigurations
Hassan Salama, Ph.DResearch associate
Karim Chatti, Ph.D
Associate professor
Michigan State University
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Background
Newly proposed Mechanistic-EmpiricalPavement Design Guide (M-E PDG) in
the U.S. does away with the ESAL
concept and uses instead axle loadspectra to calculate pavement damage
Therefore, it is important to evaluate
pavement damage caused by multiple
axles.
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Background ME-PDG Procedure
Sum the strain values ?
Ignore the strain rate ?
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Background
Two approaches for rutting prediction
Rutting at surface of subgrade layer only
Asphalt Institute (AI) model (Shook et al., 1982)
Shell Petroleum model (Claussen et al., 1977)
Rutting contribution from all pavement layers
New M-E PDG (AC and unbound materials)
VESYS rutting model
( ) * *n np e
=
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VESYS Rutting Model
( ) ( ) ( ) ( )
( ) ( )
AC base
SG
1 1AC basep AC ,AC base ,base
1 1AC base
1SGSG ei,SG
1SG
1- 1-
1-
K K
i ei i eii i
K
ii
h n h n
h n
= =
=
= +
+
p
= Constant indicating the rate of rutting decrease as the number= Constant indicating the rate of rutting decrease as the number of loadof load
applications increases.applications increases.
= Constant of proportionality between plastic and elastic strain= Constant of proportionality between plastic and elastic strain, and, and
= Compressive vertical elastic strain at the middle of the layers,e
= Number of load applications,n
= Layer thickness for AC, combined base and subgrade layers, respectively (mm),
= Number of axle groups,K
= Subscript indicating axle group,i
= Total cumulative rut depth (mm),
h
PDPsPDPs
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VESYS Rutting Model Calibration
The most likely solution for PDPs ( & )
obtained for 109 pavement sections withinthe SPS-1 experiment based on the analysisof transverse surface profile
(Salama et al, 2006 TRB publication)
Material properties, structural and climaticdata were introduced into the multiple linearregression models
(Salama et al, 2006 TRB presentation)
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Multiple Linear Regression Models for PDPs
( )0.555 1.013 0.58 0.732
105105.124* * *( ) *( )HMA Strain P VFA MAA T =
4.102 0.2136.746 * *HMA AC FI
=
0.0985 0.102 0.066 1.9822002.724*10 *modulus *Thickness * *base P GI =
3 0.808 0.8096.2567.1977 *10 * *Thickness *strainbase base =
5 0.043 1.89 0.116 0.036 0.3260.14321.385 10 * * * * * * wet daysSG
strain GI PI D FI =
304.1*594.22*764.0*41.2mod*6310*575.2 PIGIstrainulusSG
=
AC
Base
SG
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AnalysisAxle and Truck configurations used in the analysis
Pavement cross-sections and moduli
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Strain Pulses under Multiple AxlesKENLAYER (Huang, 1993)
Single axle 13 kips & tire pressure 100 psi
Multiple axle Multiple of 13 kips & spacing 42
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Strain Pulses for Thick Pavement
0.0E+00
5.0E-05
1.0E-04
1.5E-04
0 200 400 600 800
Distance, in
Strain
0.0E+00
5.0E-05
1.0E-04
1.5E-04
0 200 400 600 800
Distance, in
Strain
0.0E+00
5.0E-05
1.0E-04
1.5E-04
0 200 400 600 800
Distance, in
Strain
8-axle groupAC layer
Base layer
SG1 layer
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Strain Pulses for Thin Pavement8-axle group
AC layer
Base layer
SG1 layer
-5.0E-050.0E+005.0E-051.0E-041.5E-042.0E-042.5E-04
0 200 400 600 800
Distance, in
Strain
-5.0E-050.0E+005.0E-05
1.0E-041.5E-042.0E-042.5E-04
0 200 400 600 800
Distance, in
Strain
-5.0E-050.0E+005.0E-051.0E-041.5E-042.0E-04
2.5E-04
0 200 400 600 800
Distance, in
Strain
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Calculated PDPs
The PDPs for the two cross-sections were calculated
from the regression equations based on pavement layer
thicknesses and moduli
Other variables were assumed at the mean values of
the range used to develop the regression equations
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Rut Damage
0.0E+00
1.0E-04
2.0E-04
3.0E-04
4.0E-04
5.0E-04
0 100 200 300 400 500 600 700 800
Distance, in
Strain
Strain underneath the axles
Strain outside the axlesStrain outside the axles
Procedure 1- strain values underneath each axle within an
axle group
Procedure 2- strain values underneath the axles andoutside the axle group until the strain becomes negligible
Strain influence curve under an 8-axle group
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Results
axlesingleatoduedepthRut
groupaxlegivenatoduedepthRut=AF
axlesingleatoduedepthRut
kgiven trucatoduedepthRut=TF
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Stan.-Axle Single Tandem Tridem Quad 8-axles
Axle configurations
Rutde
pth,in
AC Base SG TotalAs an exampleAs an example
Total and per layer rutdepth for axles due to
one million repetitions
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Procedure 2
Axle factors - section 1
Truck factor - section 1
Axle factors - section 2
Truck factor- section 2
0.0
1.02.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
Single Tandem Tridem Quad 8-axles
Axle configurations
Axlefactor
.
AC Base SG Total
0.0
1.02.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
Single Tandem Tridem Quad 8-axles
Axle configurations
Axlefactor
.
AC Base SG Total
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
S5 S1T2 S1T2Tr2 S3T2Q1 S1T1E1
Ttruck configurations
Truckfactor
.
AC Base SG Total
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
S5 S1T2 S1T2Tr2 S3T2Q1 S1T1E1
Truck configurations
Truckfactor
.
AC Base SG Total
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Laboratory Results
Sample preparation Unconfined cyclic
compression load test set up
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Loading and unloading time
tS 9 tS tS 9 tS tS 9 tS time
Stress
9 tT tT 9 tT tT 9 tTtT
Sustain stress
Stress
time
1
2
Interaction= 1/2
time9 tQtQ9 tQtQ9 tQtQ
Stress
timetS1T1E1 9 tS1T1E1 tS1T1E1
Stress
Single axle
Tandem axle
Quad axle
Truck S1T1E1
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Laboratory Axle Factor
R2= 0.98
0
1
2
3
45
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10
Axle configuration
Axle
factor
Identity line
axle group single axle
axle group
single axle
1
Damage of the axle group=
1Damage of the single axle
f f
f
f
N NAF
N
N
= =
Near proportionality of rut damage for multiple axlesNear proportionality of rut damage for multiple axles
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Laboratory Axle factors
R2= 0.97
0
1
2
34
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10
Axle configuration
Axlefactor
Identity line
R2= 0.98
0
1
2
34
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10
Axle configuration
Axlefactor
Identity line
Fatigue Rutting
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Comparison with M-E PDG Prediction Tandem Axle
0.0
0.5
1.0
1.5
2.0
2.5
Lab
M-EP
DG
procedure
M-EP
DG
Softw
are
Lab
M-EP
DG
procedure
M-EP
DG
Softw
are
Method of calculating Axle Factor
A
xleFactor
RuttingFatigue
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Laboratory Truck Factortruck single axle
truck
single axle
1
Damage of the truck=
1Damage of the single axle
f f
f
f
N NTF
N
N
= =
02468
10121416
S5
S5
S1T2
S1T2
S1T2Tr2
S1T2Tr2
S3T2Q1
S3T2Q1
S1T1E1
S1T1E1
Truck configurations
Truc
kfactor
. 5-axles 11-axles
variable rest periods between axle groups affect the cumulativevariable rest periods between axle groups affect the cumulative rutrutdamage differentlydamage differently
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ConclusionsThere is little to no interaction between
axles for vertical strains within the AC layer
The interaction between axles in the base
layer increases with increasing AC layerthickness
There is always high interaction betweenaxles in the subgrade layer vertical strainresponse
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ConclusionsMechanistically, Rutting damage is
proportional to the number of axles within
an axle group or truck
Laboratory results confirmed the near
proportionality of rut damage for multipleaxles
For trucks, the variable rest periodsbetween axle groups appear to affect thecumulative rut damage differently
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Thank you!
Any questions?